if a is equals to X such that X belongs to natural numbers and X is less than 20 and b is equals to X such that X belongs to N and X is less than or equal to 5 then write the set a minus b in the set builder form
Answers
Question:
If A = { x : x € N and x < 20 } and
B = { x : x € N and x ≤ 5 } .
Write the set (A - B) in the set builder form.
Answer:
A - B = { x : x € N and 6 ≤ x ≤ 19 }
OR
A - B = { x : x € N and 5 < x < 20 }
Note:
• Set :-
A set is a well defined collection of distinct objects.
• Methods of representing a set :-
i. Roster or tabular or listed form
ii. Set-builder form
• Roster form :-
✓ All the elements are listed.
✓ Elements are separated by commas .
✓ Elements are enclosed within braces { } .
✓ The order of writing elements doesn't matter.
✓ The elements are not repeated.
• Set-builder form :-
✓ The common properties of elements are written.
✓ The elements are described using symbols like x,y,z (mostly described by x).
✓ Whole description of elements are enclosed within braces { } .
• Difference of sets :-
✓ The difference of two sets A and B in the order (also called "relative complement of B in A") is the set of all those elements of set A which are not the elements of set B.
✓ It is denoted by (A - B).
Solution:
We have two sets A and B in their set-builder form as;
A = { x : x € N and x < 20 }
B = { x : x € N and x ≤ 5 }
Here,
The roster form of the given sets A and B will be given as;
A = { 1,2,3,...,19 }
B = { 1,2,3,4,5 }
Now,
The difference of sets A and B in order will be given as ;
=> A - B = { 1,2,3,..,19 } - { 1,2,3,4,5 }
=> A - B = { 6,7,8,...19 }
Hence,
The difference set (A - B) in roster form is ;
A - B = { 6,7,8,...19 }.
Now,
The difference set (A - B) in set-builder form will be given as ;
A - B = { x : x € N and 6 ≤ x ≤ 19 }
OR
A - B = { x : x € N and 5 < x < 20 }
Hence,
Required difference set in set-builder form is;
A - B = { x : x € N and 6 ≤ x ≤ 19 }
OR
A - B = { x : x € N and 5 < x < 20 }